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dlaein.f(3) LAPACK dlaein.f(3)

NAME

dlaein.f -

SYNOPSIS

Functions/Subroutines


subroutine dlaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO)
DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

Function/Subroutine Documentation

subroutine dlaein (logicalRIGHTV, logicalNOINIT, integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionWR, double precisionWI, double precision, dimension( * )VR, double precision, dimension( * )VI, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( * )WORK, double precisionEPS3, double precisionSMLNUM, double precisionBIGNUM, integerINFO)

DLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

Purpose:


DLAEIN uses inverse iteration to find a right or left eigenvector
corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
matrix H.

Parameters:

RIGHTV


RIGHTV is LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.

NOINIT


NOINIT is LOGICAL
= .TRUE. : no initial vector supplied in (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).

N


N is INTEGER
The order of the matrix H. N >= 0.

H


H is DOUBLE PRECISION array, dimension (LDH,N)
The upper Hessenberg matrix H.

LDH


LDH is INTEGER
The leading dimension of the array H. LDH >= max(1,N).

WR


WR is DOUBLE PRECISION

WI


WI is DOUBLE PRECISION
The real and imaginary parts of the eigenvalue of H whose
corresponding right or left eigenvector is to be computed.

VR


VR is DOUBLE PRECISION array, dimension (N)

VI


VI is DOUBLE PRECISION array, dimension (N)
On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain
a real starting vector for inverse iteration using the real
eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI
must contain the real and imaginary parts of a complex
starting vector for inverse iteration using the complex
eigenvalue (WR,WI); otherwise VR and VI need not be set.
On exit, if WI = 0.0 (real eigenvalue), VR contains the
computed real eigenvector; if WI.ne.0.0 (complex eigenvalue),
VR and VI contain the real and imaginary parts of the
computed complex eigenvector. The eigenvector is normalized
so that the component of largest magnitude has magnitude 1;
here the magnitude of a complex number (x,y) is taken to be
|x| + |y|.
VI is not referenced if WI = 0.0.

B


B is DOUBLE PRECISION array, dimension (LDB,N)

LDB


LDB is INTEGER
The leading dimension of the array B. LDB >= N+1.

WORK


WORK is DOUBLE PRECISION array, dimension (N)

EPS3


EPS3 is DOUBLE PRECISION
A small machine-dependent value which is used to perturb
close eigenvalues, and to replace zero pivots.

SMLNUM


SMLNUM is DOUBLE PRECISION
A machine-dependent value close to the underflow threshold.

BIGNUM


BIGNUM is DOUBLE PRECISION
A machine-dependent value close to the overflow threshold.

INFO


INFO is INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; VR is set to the
last iterate, and so is VI if WI.ne.0.0.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 172 of file dlaein.f.

Author

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Tue Sep 25 2012 Version 3.4.2